Electrical Engineering. Example: x'yz' + xyz for the Sum-of-minterms Terms should be written in ascending order. For the terms, just write the numbers separated by commas, no space (For example: 1,2,3,4) Sum of Minterms = Product of Maxterms = QUESTION 11 Simplify the following Boolean function, using three-variable maps: F(x,y,z) = (0,2,4,5) Choose the correct answer below, and show the work on the submitted worksheet. 2. Demonstrate by means of truth tables the validity of the following identities: The distributive law: x + yz= (x+y) (x+z) 2. 9 cs309 G. a) 3 Variables: A (x,y,z) = m0 + m5 + m6 + m7b) 3 Variables: B (x,y,z) = m0 + m2 + m3 + m5 + m6 + m7c) 4 Variables: 𝐶 (𝑤, 𝑥, 𝑦. So how can we show the operation of this “product” function in Boolean Albegra. See the difference between the two expressions, the truth table, the K-map and the model answer for this question on Stack Overflow. . The sum of all such terms is called a Standard Sum of Product. (e) Simplify E and Fto expressions with a minimum of literalsQ: Express each of the following function as a sum of minterms and as a product of maxterms F = x′z +… A: As given, I need to express the given functions as a sum of minterms and product of maxterms. Any Boolean function can be expressed as a sum of its 1-minterms and the inverse of the function can be expressed as a sum of its 0-minterms. . So, A and B are the inputs for F and lets say, output of F is true i. 10 of a logic function f of three variables. Show transcribed image text. which implies that the minimal sum-of-products is given by f = x1 x3' + x2' x3. Sum of Minterms or SOM is an equivalent statement of Sum of Standard products. In this lesson, we will look at one of two "standard forms" of boolean functions. Use only NAND gates in your design. The sum of minterms, known as the Sum of Products (SOP) form, is a simplified version of a Boolean function represented as an OR combination of minterms. we need to simplify the function in the sum of minterms we will use the K-Map to simplify the function the K-Map is a very useful tool to simplify long boolean expressions into simplified form in a very systematic approachKarnaugh map can produce Sum of product (SOP) or product of Sum (POS) expression considering which of the two (0,1) outputs are being grouped in it. Since any boolean function can be expressed as a sum of minterms, a decoder that can generate these minterms along with external OR gates that form their. For the following functions, show an algebraic expression in sum of minterms form. The DNF is simply, wxyz + wxyz + wxyz + wxyz + wx yz + wxy z + wxy z + wx y z 12. Find the Sum-of-Minterms canonical Boolean expression for the output signal B. (A. Find the sum-of-products expansion of the Boolean function F(w;x;y;z) that has the value 1 if and only if an odd number of w;x;y, and z have the value 1. Who are the experts? Experts have been vetted by Chegg as specialists in this subject. Reset Terms. Here you can see a sum of two terms. Therefore, the SOP form is: F(A, B,. (a) List the minterms and maxterms of each function. • In Minterm, we look for the functions where the output results is “1”. Note: For n-variable logic function there are 2 n minterms and 2 n maxterms. e. Sum of Minterms or SOM is an equivalent statement of Sum of Standard products. B’ 1 1 m3 = A . . Question: 2-11. Once again, the numbers indicate K-map cell address locations. CSE370, Lecture 51 Canonical forms! Last lecture " Logic gates and truth tables " Implementing logic functions " CMOS switches Today™s lecture " deMorgan™s theorem " NAND and NOR " Canonical forms #Sum-of-products (minterms) #Product-of-sums (maxterms) 2 de Morgan™s theoremObtain the truth table of the following functions and express each function in sum of minterms and product of maxterms: a) (xy + z) ( y + xz) b) (A’+ B) (B’+C) c) y’z + wxy’ + wxz’ + w’x’z 3. (b) Determine the sum of minterms expression. a). . Expert-verified. Please clearly show your Karnaugh maps, circling, and place your final Boolean equation on the line provided. Analysis: F(A, B, C) = AB + BC̅ + AC̅. My method of finding them, however, is wrong, because the minterms are actually 0,3,5, and 7. F(x,y,z) = xyz Is the given equation in the canonical sum of minterms form? If not, convert it into this form. List the. Obtain the function F as the sum of minterms from the simplified expression and show that it is the same as the one in part (a) e. For each input/output table, give a Boolean expression that is a sum of minterms and is equivalent to the function defined by the table. as well as the minterms they are covering need to be taken out of the prime implicants chart. How do you find the function of Boolean expression? Each Boolean expression represents a Boolean function. . 1. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. It is used for finding the truth table and the nature of the expression. ms + m + m² Cdim - m₂ + m7. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. A Karnaugh map (K-map) is an abstract form of ____________ diagram organized as a matrix of squares. And what is minterm. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. ) a. . ) Convert the following Boolean function from a sum-of-minterms form, to a product-of-sums form: F (w,x,y,z) = ∑(0,1,2,5,8,10,13) 2. Minterm is the product of N distinct literals where each literal occurs exactly once. Express the following Boolean functions in both sum of minterms and product of maxterms forms: Introductory Circuit Analysis (13th Edition) 13th Edition. Identifying the Minterms from the K-map is equivalent to reading equations in Sum-of-Minterms or Sum-of-Products (SOP) form, directly from the truth table. 2. Construct the truth table of the function, but grouping the n-1 select input variables together (e. (cd+b′c+bd′) (b+d) 3. Step 1. Question: CHALLENGE ACTIVITY 1. Trending now This is a popular solution! Step by step Solved in 2 steps. Question: a. an implicant with the fewest literals. I must solve this by using boolean algebra rules but i dont know how. Given the timing diagram shown in Figure P2. so, we have x, y, x’ and y’. Minterms are single 1s in a map, maxterms are 0s in a map. ISBN: 9780133923605. . These are used in POS. 17 Obtain the truth table for the following four-variable functions, and express each function in sum-of-minterms and product-of-maxterms form: (a)* (ac. To grasp this concept fully, Table 1. [c] Write the short form Sum of Products (SOP) expression (list minterms). Digital Circuits Questions and Answers – Karnaugh Map. F = ABC + ABD + ABC + ACD (b) F= (W+X+Y) (WX + Y. Set the rising edges of a to be reference lines. It can be directly taken from the Truth Table for the function. A*B = A and B. F (a,b,c)=ab′+c′a′+a′ B. Q1. Express function in canonical sum-of-minterms form. A 2-variables function has 2 2 =4 possible maxterms. but it's useful to be able to do this in 1 step. When we write the truth table and see for which cases the value of F evaluates to 1, we get multiple cases. Example 2. However, the inverse function will be directly expressed as a sum of minterms (‘sum of products’, ‘S-of-P’ or ‘SOP’ form) which can then be plotted immediately. For example, consider the truth table in Figure 3. Question: Identify the Boolean function that is defined by the following input/output table. If the variable value is 0, take its complement. ). Once again, the numbers indicate K-map cell address locations. Though, we do have a Sum-Of-Products result from the minterms. Q. Express the complement of the following functions in sum‐of‐minterms form:The outputs are E and F. Convert to sum-of-minterms form: bc+b'c 3 = Ex: xyz + xyz' + xy'z + xyz Use the true form of the literal first when expanding. 1a, it is possible to represent only 14 minterms. Express f (x, y, z) = x y ˉ + x ˉ yz as a canonical SOM. Engineering. To understand better about SOP, we need to know about min term. f. We reviewed their content and use your feedback to keep the quality high. Complement function will be equal to the sum of minterms missing from the given function. A maxterm is a sum. Example. Now we have to obtain the PDNF (Principal disjunction normal form) and PCNF (Principal conjunction normal form) with the help of equivalence. Suppose n = 2 (x and y) and, we know ‘0’ represents complements i. A city water service has a base cost of $12 per month plus$1. Maxterm can be understood as the sum of Boolean variables (in normal form or complemented form). Electrical Engineering. Solution: = x + y z = x + (y z) AND (multiply) has a higher precedence than OR (add) = x(y+y')(z+z') +. Example of POS: (X+Y) (X’+Y’) Explanation:Call for mincalc mincalc Data vectors are linearly independent Computable target probabilities 1. Implement the sum of minterms of this function and connect a, b, c and d to clock. 4. Transcribed image text: Q7 4 Points The following questions refer to the Truth Table below Q7. F=x'yz'+xy'Z'+xy'Z+xyz'+xyz b. Groups must be a power of 2. In addition, you must show your work on the paper you submit on eLearning to get credit. 1 Answer. See Answer See Answer See Answer done loadingDigital Circuits Questions and Answers – Karnaugh Map. 2. Input Variable (A) Input Variable (B) Minterm Minterm notation. Groups must be a power of 2. 6(3)(English) (Morris Mano) Question 2 . • Each individual term in the SOP form is called Minterm. AB̅C + A̅B̅C +. 2. The grouping of 0’s result in Product of Sum expression & the grouping of 1’s result in Sum of Product expression. Both have their uses depending on the situation. – A function can be written as a sum of minterms, which is referred to as a minterm expansion or a standard sum of products. It represents exactly one combination of binary variable values in the truth table and it has the value 1 1 1 for that combination. Chap 4 C-H5 Minterm/Maxterm Three variables . A Karnaugh map (K-map) is an abstract form of ____________ diagram organized as a matrix of squares. You answer should be in the format of sum of minterms. x’ and y’. Simplify E and F to expressions with a minimum of literals. • Minterms that may produce either 0 or 1 for the function. We illustrate the fundamental patterns in the case of four events ({A, B, C, D}). Obtain the truth table for the following functions, and express each function in sum-of-minterms and product-of-maxterms form: ( b + c d ) ( c + b d ) Expert Solution. and that "A compact notation is to write only the numbers of the minterms included in F" which is $\sum (1,2,4,7)$ I don't understand this because the rows in the truth table are interchangeable; 0,0,0,0 could be the last row instead of the first. Question: Expand wy to sum-of-minterms form wyz+wyz' 1. Support Simple Snippets by Donations -Google Pay UPI ID - tanmaysakpal11@okiciciPayPal - paypal. Table 1: Truth table for the NAND circuit 1. So the minterms would come out to be 0, 1, 1, 3, 5, and 7. I want to ask that if we are told to express an Boolean Expression in sum of min-terms which is already in non-standard SOP form. F (a,b,c,d)=b (ac+a′c′)+a′d D. A function that defines the solution to a problem can be expressed as a sum of minterms (SoM) in which each of the minterms evaluates to \(1\text{. The truth tables for the minterms and maxterms are as follows: Minterms: Maxterms: Explanation: To find the canonical form for the SOP (sum of minterms), we need to identify the minterms where the function evaluates to 1. Question: Express the following function as a sum of minterms and as a product of maxterms: F(A,B,C,D) = B'D + A'D + BD For example: (1,2,3,4) Sum of Minterms. 0 1 02 03. We count the number of “successes” corresponding to each minterm by using the MATLAB function sum, which gives the sum of each column. Max terms result in zeros and include all the remaining cells except don’t cares. Here’s the best way to solve it. 17 Obtain the truth table for the following functions, and express each function in sum-of minterms and product-of-maxterms form: (a)" (b + cd) (c + bd) (b) (cd + b'c + bd' (b + d) (d) bd'+ acd'+ ab'c+ a'c. Computer Science. It is calculated as the. w=xy+x′yz+y′z′ b. Step 3. 7. The following are examples of “simplifying” that changes a. 382370. Describes how to derive the Sum of minterms from a three variable Truth TableIn Sum of Products (what you call ANDs) only one of the minterms must be true for the expression to be true. Why do we need minterms in the first place? We do not need minterms, we need a way to solve a logic design problem, i. The above equation can be rewritten in m-notation, f (A, B, C) = m 3 + m 4 + m 5 + m 6 + m 7 f (A, B, C) = Σ m (3,4,5,6,7) ECEN 1521 Page 4 of 14Question 4: Determine the truth table for each of the following functions and express the function in both sum-of-minterms and product-of-maxterms form: (a) F(a,b,c,d. Any Boolean function can be expressed as the sum (OR) of its 1- min terms. a) The Boolean function E = F 1 + F 2 containsthe sum of minterms of F 1 and F 2. 1: Convert the table to a sum-of-minterms. given a truth table, find a logic circuit able to reproduce this truth table. See Answer See Answer See Answer done loadingObtain the truth table for the following functions, and express each function in sum-of- minterms and product-of-maxterms form: (Total: 30 points) (a) F(X, Y, Z) = XY' + X'Y + XZ' + X'z 1. Therefore M i = m’ i. Q7. Example: The output values are 0,1,1,0, (and the table is ordered from 00 to 11), so the truth table is: input. Each variable in a Boolean expression can hold only one value out of two: 1 for all truthy values and 0 for all falsy values. Minterms are represented in the SOP. There are 2 cases when f is false: Not f = (Row 3) Or (Row 4) = AB¯¯¯¯C Or AB¯¯¯¯C¯¯¯¯. Show a minimum SOP expression (f. Obtain the truth table of the following functions, and express each function in sum‐of‐minterms and product‐of‐maxterms form: (a) (b + cd)(c + bd)(a) Express X as a sum-of-minterms and product-of-maxterms (b) Express Y as a sum-of-minterms and product-of-maxterms 4. Each is worth 3. Since the number of literals in such an expression is usually high, and the complexity of the digital logic gates that implement a Boolean function is directly related to the complexity of the. 12. Convert to sum-of-minterms form: ac + a'c' Here’s the best way to solve it. – A function can be written as a sum of minterms, which is referred to as a minterm expansion or a standard sum of products. It should be noted that the minterms whose sum helps in defining the Boolean function will be the ones that give the 1's with regards to the functions in the truth table. Simplify the. 0000 0. Therefore, F = m3 + m4 + m5 + m6 + m7, which is the same as above when we used term expansion. Question: For the input/output table, give a Boolean expression that is a sum of minterms and is equivalent to the function defined by the table. #Minterms #Maxterms #Representhegivenbo. Write the following expression as a sum of minterms: f(x,y,z)=xyz^'+x^' z+y, then simplify. 0-minterms = minterms for which the function F. It is called a canonical or standard sum because each variable, either in true form or complemented form, appears once. The boolean algebra calculator is an expression simplifier for simplifying algebraic expressions. A device used in cases where only 2 people work in a business where A. Engineering. F (W, X, Y, Z) = (1, 3, 4, 9, 11, 14, 15) + d (2, 8) a)Obtain the list of all prime. The representation of the equation will be Thus, the minterms form a partition. Now apply DeMorgan's: Not Not f f = Not (AB¯¯¯¯C Or AB¯¯¯¯C¯¯¯¯) = (A¯¯¯¯ Or B Or C¯¯¯¯) And (A¯¯¯¯ Or B Or C) Your given answer for "product of maxterms. Logic circuit design | minterm and Maxterm and SOP and POS الحصول علي محتويات الفيديو 00:00 - البداية00:08 - minterm and. The Sum of Product (SOP) form 2. )). The Product of Sum (POS) form . Sum of minterms form •Every function can be written as a sum of minterms, which is a special kind of sum of products form •The sum of minterms form for any function is unique •If you have a truth table for a function, you can write a sum of minterms expression just by picking out the rows of the table where the function output is 1. Only (0+0+0)=0 will equal 0. The minterms, 1 s, in the map have been grouped as usual and a Sum-OF-Products solution written. Product-of-maxterms 3. 50 per hundred cubic feet (HCF) of water. Click Apply property 4. 3, note that minterm 0 (000 2) is just above minterm 4 (100 2). w=y+xy′z′+xz+x′y′z ick or tap here to enter text. Make rectangular groups. Show transcribed image text (a) Construct the truth table. A Product-OF-Sums solution is completed in the usual manner. , logical-AND) of all of the signals, using the complement of any signal that needs to be False for that combination of inputs. There are 2 steps to solve this one. (e) Simplify E and F to expressions with a minimum of literals. F (a,b,c) = a'c' + a'c + bc'. This product is not arithmetical multiply but it is Boolean logical AND and the Sum is Boolean logical OR. Final answer. • while in Maxterm we look for function where the output results is “0”. Show and explain the completed circuit. The output of the minterm functions is 1. Express the complement of the following function in sum of minterms: a) F(A,B,C,D)=∑(0,2,6,11,13,14) b) F(x,y,z)=∏(0,3,6,7)This video provides the solution to the problem: 2. The important points to note are that the fundamental product terms specify where the minterms are in the final map, whereas the fundamental sum terms specify where a zero appears in the final map. 19: Express the following function as a sum of minterms and as a product of maxterms: F(A,B,C,D) = B'D + A'D + BDPlease subscribe to my channel. Obtain the truth table of F and represent it as sum of minterms b. 3. As discussed in the “Representation of Boolean Functions” every boolean function can be expressed as a sum of minterms or a product of maxterms. Maxterm. Each of these three product statements is a minterm—a term that is True (1) for exactly one combination of inputs. The boolean algebra calculator is an expression simplifier for simplifying algebraic expressions. Tour Start here for a quick overview of the site Help Center Detailed answers to any questions you might have Meta Discuss the workings and policies of this site-SUM OF MINTERMS-MAXTERMS-PRODUCT OF MAXTERMS • Given an arbitrary Boolean function, such as how do we form the canonical form for: • sum-of-minterms • Expand the Boolean function into a sum of products. Example − AB ′ C is a Boolean expression. Previous question Next question. 1b it is impossible to represent the minterms x1 x2 x3' x4' and x1 x2 x3 x4'. Maxterm. Here’s the best way to solve it. 1: Write in sum-of-minterms form. b) (cd + b'c + bd' ) (b + d) Expanding it we get : =>. 2. • Any combinational circuit with n inputs and m. Expert Answer. 3. Be able to use both alphabetic and decimal notation. Chap 4 C-H6. These are used in POS. Electrical Engineering. Electrical Engineering questions and answers. Write a function f(x) to represent the cost of water as a function of x, amount used. A minterm, denoted as mi, where 0 ≤ i < 2n, is a product (AND) of the n variables in which each variable is complemented if the value assigned to it is 0, and uncomplemented if it is 1. Question: Write the following expression as a sum of minterms: f(x,y,z)=xyz^'+x^' z+y, then simplify. Example if we have two boolean variables X and Y then X + (~Y) is a maxterm we can express complement ~Y as Y’ so, the above maxterm can be expressed as X + Y’ So, if we have two variables then the maxterm will consists of sum of both the variables. Express f (x, y, z) = x ˉ + y ˉ z as a canonical SOM. 2. A*B = A and B. (a) (a + b + c) (a'b' + c) (b) h'bc + abc' + abc + a'bc' (c) (a + c) (a + b' + c') (d. Example 2. me/tanmaysakpal11-----. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Minterms are represented in the SOP. F(a, b, c) = (A & B & C) | (A & B & (~C)) | (A & (~B) & C) | (A & (~B) & (~C)) which is then perfectly simplified to F(a, b, c) = AWe generally use the ∑ (sigma) notation to represent minterms. How Does the Sum of Minterms Calculator Work? This online calculator simplifies the process of finding the sum of minterms or SOP for any logical expression or truth table. Literal – x, y, A, b etc is a label which denote an input variable for a logic gate. The following questions refer to the Truth Table below Q7. This form is obtained by identifying minterms (where output is 1) in a truth table and combining them using the logical OR operator. DNF and CNF missing law/rule. Steps to Solve Expression using K-map. 2120130. One way to get the SoP form starts by multiplying everything out, using the distributive law: (ac + b)(a + b ′ c) + ac = ac(a + b ′ c) + b(a + b ′ c) + ac = aca + acb ′ c + ba + bb ′ c + ac = ac + ab ′ c + ab + ac = ac + ab ′ c + ab. Show 0 1 1 0 0 6 5 4 10001 10111 1 1 0 1 1. F = ab' + bc + a'bc a b. Draw circuit in Logisim. A minterm is a product of all variables taken either in their direct or complemented form. Referring to the above figure, Let’s summarize the procedure for writing the Sum-Of-Products reduced Boolean equation from a K-map: Form largest groups of 1s possible covering all minterms. Observe the table, if the minterm is covered by only one prime implicant then it is an essential to prime implicant. Obviously, this requires a methodology. A. View the full answer. In Figure P2. Show a minimum SOP expression (a: 2 terms, 5 literals; b: 1 term, 1 literal). Answer to Solved Example 3. 2 is the complement of the corresponding minterm A B ¯ C Plotting a maxterm on a Karnaugh map requires further consideration. 2. The sum of minterms is called a Canonical Sum of Product. Using DeMorgan’s law, write an expression for the complement of F. It is a product of all variables in a function and that function has the property that it is equal to 1 on exactly one row of the truth table. Suppose Limor Fried expands her business, Adafruit Industries, to make electric scooters. The answer should list the minterms as m0+m1+m2. Show 0 1 1 0 0 10001 10111 1 1 0 1 1 11110. List the minterms of E- and F-. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. b) F(az, Y, 2) = I(3, 5, 7) 5. The Boolean function G=F1F2 contains only the minterms that are common to F1 and F2. Any boolean function can be represented in SOM by following a 2 step approach discussed below. Question: Express the following Boolean function as a sum of minterms. There was no reduction in this example. Example of SOP: XY + X’Y’ POS: Product of sums or product of max terms. Show the un-simplified logic equation for the customizedfunction, expressed as a sum of minterms. Please clearly show your Karnaugh maps, circling, and place your final Boolean equation on the line provided. o Example, where n=3 and the variables are x, y and z:. 2. 2: Representing a Boolean function by a sum of minterms. 4 Points. 1 Using truth tables, express each one of the following functions and their complements in terms of sum of minterms and product of maxterms. Show an algebraic expression in sum of minterms form. Here’s the best way to solve it. Since any boolean function can be expressed as a sum of minterms, a decoder that can generate these minterms along with external OR gates that form their logical sums, can be used to form a circuit of any boolean function. Its De Morgan dual is a " Product of Sums " ( PoS or POS) for the canonical form that is a conjunction (AND) of maxterms. Expert Answer. net dictionary. So the minterms would come out to be 0, 1, 1, 3, 5, and 7. You can do it this was as well, but it is equivalent to the algebraic expansion that you already did. Literal can. – A function can be written as a product Canonical Sum or Sum of Minterms (SoM) a sum of products in which each product term is a minterm. The same concept applies for Canonical Product of Sum form. Refer minterms from here. Expert Answer. Q: Express each of the following function as a sum of minterms and as a product of maxterms F = x′z +… A: As given, I need to express the given functions as a sum of minterms and product of maxterms. For the Boolean functions F(X,Y,Z) and E(X,Y,Z), as given in the following truth table: (a) List the minterms of F(b) List the maxterms of E(c) List the minterms of E' (d) List the maxterms of F⋅E(e) Express the Standard Sum of Product (SSOP) form of F(f) Express the Standard Product of Sum (SPOS) of F⋅EThis problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Don't Cares: Comma separated list of numbers. Simplify the given function using K-Map. Applies commutative law, distributive law, dominant (null, annulment) law, identity law, negation law, double negation (involution) law, idempotent law, complement law, absorption law, redundancy law, de. Exercise 5. The given expression can be written as:Question: Consider a function with three variables: a, b, c. • Each individual term in the SOP form is called Minterm. We reimagined cable. Using the minterms for which the function is equal to 1, the function can be written explicitly as follows: Minterms. Sum of the Minterms = Sum-of. Given the circuit below: [a] Write the switching expression for the circuit in 2-level AND-OR format [b] Use the AND-OR expression to enter the minterms (1 cells) into a 4-variable K-Map. This problem has been solved! You'll get a detailed solution from a subject matter expert that helps you learn core concepts. Also, Boolean functions can be simplified using Karnaugh map ( K - map) without using Boolean theorems, by transferring a function to K-map and reading simplified function from K-map. A sum-of-products form must be a sum of minterms and a minterm must have each variable or its compliment as a factor. Canonical Sum of Products. Design a logic circuit using a minimum number of 3 -to-8 decoders (74LS138) and logic gates that does the following: a. Electrical Engineering questions and answers. 3. • These don’t-care conditions can be used to provide further simplification of the algebraic expression. Maxterm. e. egin {tabular} {|c|c|c|} hlinex & y & f (x,y) hline 0 & 0 & 1. A prime implicant is an implicant of minimal size (i. Sum of minterms or also the sum of products for which the function takes 1 in the truth table, it is the sum of standard product terms linked by an OR operator: f = a. So a 4-variable k-map will have 16. Sum-of-minterms 2. Develop a truth table for a 1-bit full subtractor that has a borrow input ºn and input * and, and produces a difference, d, and a borrow output, Pout. Simplify the following Boolean expressions to a minimum number of literals. 3. The following are examples of “simplifying” that changes a.